In logic, begging the question is the term for a type of fallacy occurring in deductive reasoning in which the proposition to be proved is assumed implicitly or explicitly in one of the premises. For an example of this, consider the following argument: "Only an untrustworthy person would run for office. The fact that politicians are untrustworthy is proof of this." Such an argument is fallacious, because it relies upon its own proposition—in this case, "politicians are untrustworthy"—in order to support its central premise. Essentially, the argument assumes that its central point is already proven, and uses this in support of itself.

Begging the question is also known by its Latin name petitio principii and is related to the fallacy known as circular argument, circulus in probando, vicious circle or circular reasoning. As a concept in logic the first known definition in the West is by the GreekphilosopherAristotle around 350 B.C., in his book Prior Analytics, where he classified it as a material fallacy.

The term is usually not used to describe the broader fallacy that occurs when the evidence given for a proposition is as much in need of proof as the proposition itself. The more accepted classification for such arguments is as a fallacy of many questions.

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The term was translated into English from the Latin in the 16th century. The Latin version, Petitio Principii (petitio: petition, request; principii, genitive of principium: beginning, basis, premise of an argument), literally means "a request for the beginning or premise." That is, the premise depends on the truth of the very matter in question.

"Begging or assuming the point at issue consists (to take the expression in its widest sense) in failing to demonstrate the required proposition. But there are several other ways in which this may happen; for example, if the argument has not taken syllogistic form at all, he may argue from premises which are less known or equally unknown, or he may establish the antecedent by means of its consequents; for demonstration proceeds from what is more certain and is prior. Now begging the question is none of these. [...] If, however, the relation of B to C is such that they are identical, or that they are clearly convertible, or that one applies to the other, then he is begging the point at issue.... [B]egging the question is proving what is not self-evident by means of itself...either because predicates which are identical belong to the same subject, or because the same predicate belongs to subjects which are identical."

Fowler's Deductive Logic (1887) argues that the Latin origin is more properly Petitio Quæsiti which is literally "begging the question" as opposed to "petitioning the premise".

"That begs the question" is an apt reply when a circular argument is used within one Syllogism. That is, when the deduction contains a proposition that assumes the very thing the argument aims to prove; in essence, the proposition is used to prove itself, a tactic which in its simplest form is not very persuasive. For example here is an attempt to prove that Paul is telling the truth:

Suppose Paul does not lie when he speaks.

Paul speaks.

Therefore, Paul is speaking truth.

These statements are logical, but they do nothing to convince one of the truthfulness of the speaker. The problem is that in seeking to prove Paul's truthfulness, the speaker asks his audience to assume that Paul is telling the truth, so this actually proves "If Paul is not lying, then Paul is telling the truth." which is nothing more than a tautology.

It is important to note that such arguments are logically valid. That is, the conclusion does in fact follow from the premises, since it is in some way identical to the premises. All self-circular arguments have this characteristic: that the proposition to be proved is assumed at some point in the argument. This is why begging the question was classified as a Material fallacy rather than a Logical fallacy by Aristotle.

Formally speaking, the simplest form of begging the question follows the following structure. For some proposition p:

p implies p

suppose p

therefore, p.

However, the following structure is more common:

p implies q

q implies r

r implies p

suppose p

therefore, q

therefore, r

therefore, p.

The syntactic presentation of the fallacy is rarely this transparent, as is shown, for example, in the above argument purportedly proving Paul is telling the truth.

In a related sense, the phrase is occasionally used to mean "avoiding the question". Those who use this variation are explaining that the argument lacks a premise, and they have missed the self-circularity of the argument because of it.

Fowler's Modern English Usage classifies begging the question in a somewhat different fashion (for example, in contrast to the meanings from Merriam-Webster, the Oxford English Dictionary, and the American Heritage Dictionary). Fowler states that it is "The fallacy of founding a conclusion on a basis that as much needs to be proved as the conclusion itself." This is more commonly known as the Fallacy of many questions.

Begging the question is related to the Fallacy of Circular Reasoning. The distinction between the two concepts is as follows: Circular Reasoning is the basing of two conclusions each upon the other (or possibly with more intermediate steps). That is, if you follow a chain of arguments, one of the conclusions is presumed by an earlier conclusion. Begging the question can occur within one argument and consequent conclusion. In the strictest sense, Begging the question occurs if and only if the conclusion is implicitly or explicitly a component of an immediate premise. It is usually accepted, though, to use the term begging the question in place of circular argument.

An example of a circular argument is as follows:

A majority of people voted that Democracy is the most effective form of determining how effective something is.

Therefore Democracy is the most effective form of determining how effective something is.

Begging the question is also related to the Fallacy of many questions—a fallacy of technique that results from presenting evidence in support of a conclusion that is logically more difficult to accept than the mere assertion of the conclusion on its own.

A specific form of this is reducing an assertion to an instance of a more general assertion which is no more known to be true than the more specific assertion:

Every intentional act of killing a human being is morally wrong.

The death penalty is an intentional act of killing a human being.

Therefore the death penalty is wrong.

If the first premise is accepted as an axiom within some moral system or code, this reasoning is a cogent argument against the death penalty. If not, it is in fact a weaker argument than a mere assertion that the death penalty is wrong, since the first premise is stronger than the conclusion.

More recently, "begs the question" has been used as a synonym for "invites the question" or "raises the question", or to indicate that "the question really ought to be addressed". In this usage, "the question" is stated in the next phrase. The following is an example: "This year's budget deficit is half a trillion dollars. This begs the question: how are we ever going to balance the budget?" This usage is often sharply criticized by proponents of the traditional meaning, but it has nonetheless come into common use.

Argument over whether this usage should be considered incorrect is an example of the debate between linguistic prescription and description.